1. Field of the Invention
An aspect of the invention relates to error correction and signal detection, and more particularly, to a method and apparatus for generating error correction parity information.
2. Description of the Related Art
A coding method using Low Density Parity Check (LDPC) codes for error correction creates a parity check code including predetermined numbers of “ones” in the rows and columns of an error correction code (ECC) block, and generates parity information using the parity check code.
More specifically, a parity check matrix H is created that includes a predetermined number of “ones” in the matrix columns and rows, and a codeword x satisfying the equation “Hx=0” is obtained. Here, the codeword x relates original data to parity information. For performing this calculation, the parity check matrix H is first transformed into a generator matrix G using Gaussian elimination, or transformed into a lower triangular form.
However, the generator matrix G requires large calculations due to the absence of sparseness of the original matrix. Also, the lower triangular form requires a complicated calculation process.
A conventional parity check matrix H is shown in FIG. 1. The following Equation (1) represents a lower triangular form of the calculation process for generating a codeword x satisfying “Hx=0”. As apparent from Equation (1), the calculation process is complicated.
                                          H            ⁡                          [                                                                                          A                      ⁢                                                                                          ⁢                      B                      ⁢                                                                                          ⁢                      T                                                                                                                                  C                      ⁢                                                                                          ⁢                      D                      ⁢                                                                                          ⁢                      E                                                                                  ]                                →                      H            ×                          [                                                                    1                                                        0                                                                                                              -                                              ET                                                  -                          1                                                                                                                          1                                                              ]                                      =                  [                                                    A                                            B                                            T                                                                                                                                -                                              ET                                                  -                          1                                                                                      ⁢                    A                                    +                  C                                                                                                                        -                                              ET                                                  -                          1                                                                                      ⁢                    B                                    +                  D                                                            0                                              ]                                    (        1        )            P1=−Φ−1[−ET−1AST+CST],φ=−ET−1B+D,P2=−T−1[AST+BP1T]
A basic concept for LDPC coding is disclosed in “Good Error-Correcting Codes Based on Very Sparse Matrices,” by D. J. C. MacKay, IEEE Transactions on Information Theory, Vol. 45, No. 2, pp. 399-431, March 1999, and a technique for coupling the parity check matrix H is disclosed in “Efficient Encoding of Low-Density Parity-Check Codes,” T. Richardson and R. Urbanke, IEEE Transactions on Information Theory, Vol. 47, No. 2, pp. 638-656, February 2001.